Last Saturday, Ahmed Hassan, a 17-year-old Muslim student, was stabbed to death in an unprovoked attack by a gang of white youths at Dewsbury railway station in west Yorkshire. Two have now been charged with his murder, and police say they are investigating whether there was a racial or religious motivation. In the Muslim communities in Dewsbury and neighbouring Batley, where Hassan lived, there's little doubt about it. In the run-up to today's Eid festival, Hassan's family issued a statement saying they hoped their loss would help "unite the community and all faiths".

But divisions run deep in the area. The far-right British National party, which has increasingly turned its racist venom against Muslims in recent years, won over 5,000 votes in Dewsbury in the last general election, its highest tally in the country. Its leader, Nick Griffin, has argued that his party must capitalise on the "growing wave of public hostility to Islam currently being whipped up by the mass media". It's not hard to see why he sees an opportunity. Since the July 2005 bombings in London, there has been a stream of sensationalised and poisonous stories about Britain's Muslims.

This media onslaught - often based on research by apparently reliable thinktanks - has clearly fed anti-Muslim prejudice. Combined with hyped terror-plot reports, the point has now been reached where Britons are found in polls to be more suspicious of Muslims than are Americans or citizens of any other major European state. For many Muslims, that heightens a sense of intimidation and alienation. For a minority, it translates into Islamophobic violence on the streets: Asian people are now twice as likely to be stabbed to death as a decade ago, and four out of five convictions for religiously aggravated offences last year involved attacks on Muslims.

But now the seamy underbelly of this dangerous campaign is coming to light. At the end of October, the influential Conservative-linked thinktank Policy Exchange published a report entitled The Hijacking of British Islam, which claimed that 26 out of nearly 100 mosques surveyed had been found to be selling "extremist material, some of it antisemitic, misogynistic, separatist and homophobic". The story was given top billing by newspapers and broadcasters. "One in four British mosques is in the grip of extremism", the Sun screamed, while the Times splashed it across its front page under the headline: "Lessons in hate found at leading mosques".

But last week, BBC's Newsnight programme - previously not shy of running inflammatory items itself on the Muslim community - revealed that a forensic examination of five receipts provided by Policy Exchange for the material had found them to be either faked, written by the same person, and/or were not issued by the mosques in question. A sixth receipt was also regarded as unreliable.

It might be supposed that receipts from the other 20 mosques were nevertheless found to be authentic and that Policy Exchange's basic case held. Not so. Newsnight didn't have the resources to check them. But it has since emerged that in one of these cases, Edinburgh central mosque, the mosque authorities insist books said by Policy Exchange to have been found there were in fact dumped in its grounds after the report was published. In another, the Times has this week had to publish an apology to East London mosque chairman Dr Muhammad Abdul Bari, after reporting Policy Exchange's claim that the mosque was selling extremist literature.

Yesterday I contacted yet another mosque, Rochdale Central, claimed by Policy Exchange to have provided a receipt for extremist literature. No, said the imam, Hafiz Ikram, "we haven't got a bookshop and we don't sell books. Once or twice a year, people set up stalls in the carpark outside the mosque after Friday prayers, but they have nothing to do with us." That makes all nine receipts so far investigated either fabricated or inaccurate.

Policy Exchange insists it is standing by its research. But, given the evidence of falsification, it clearly cannot be regarded as reliable, nor can there be any confidence that the mosques supposedly surveyed were a representative sample. The thinktank has form in this area: earlier this year, the methodology and reliability of another heavily publicised report on Muslim separatism came under heavyweight academic attack. But it was still used by David Cameron to rubbish multiculturalism.

Charles Moore, Policy Exchange's chairman and former Daily Telegraph editor, claims Newsnight "told a small story" about dodgy receipts to "kill a much bigger story" - that "extremist literature was available in the mosques". But the extent of that availability is crucial: one of Policy Exchange's researchers told Newsnight they had had to go back three times to get hold of books. Of course, there are plenty of ultra-conservative and reactionary religious Islamic texts in circulation (though little of what Policy Exchange identified had anything to do with jihad) and those are most effectively challenged by other Muslims. You can also see ugly material in other religious institutions, such as the aggressively homophobic pamphlets I recently found on display in a south-west London church.

But the exaggeration of such phenomena and constant regurgitation of Muslim-baiting "research" by hard-right thinktanks like Policy Exchange and the Centre for Social Cohesion misleads the public and inflames ethnic tensions. It is also transparently driven by a neoconservative agenda that seeks to convince people that jihadist terror attacks in Britain are fuelled not by outrage at western violence and support for tyranny in the Muslim world, but by hatred of western culture and freedoms.

The roll call of those involved in Policy Exchange makes the point. Its policy director, Dean Godson, who blustered at Newsnight's presenter Jeremy Paxman last week, worked for the Reagan administration, was a signatory to the neocon Project for the New American Century, and was special assistant to the jailed former Telegraph owner Conrad Black. The report's author is Denis MacEoin, a pro-Israel campaigner who says he has "very negative feelings" about Islam. The thinktank's founders were Nicholas Boles, now Tory candidate for Grantham, and Michael Gove, author of that British neocon rallying cry Celsius 7/7 and now the Tory education spokesman. If Cameron cares anything for community relations, he should rein in these toxic attack dogs.